If I buy the Enhanced Edition to play on my Windows 10 computer and GOG updates it to play on a Windows 11 computer, will I have to pay again? I really want to play this on my Windows 11 computer because of issues on my Windows 10 computer.

Umm.. no. Once you've bought a Windows game, it doesn't which version of Windows you want to play it on. You don't have to pay for it again. All the GOG updates for the games are also free. The only exception is if "Enhanced Editions" of games come out, you'll have to buy them once, even if you previously bought the original version of the game prior to it.